List the hydrogen halide acids in decreasing order of reactivity in the following reaction `R-OH+HXrarrRX+H_2O`

Options

A. `HI gt HBr gt HCl gt HF`
B. `HBr gt HCl gt HCl gt HF`
C. ` HI gt HCl gt HBr gt HF`
D. `HI gt HF gt HBr gt HI`

Answer

To determine the order of reactivity of hydrogen halide acids (HX) in the reaction \( R-OH + HX \rightarrow RX + H_2O \), we need to analyze the strength of the acids and their corresponding conjugate bases. The hydrogen halides we are considering are HI, HBr, HCl, and HF.

### Step-by-Step Solution:

1. **Identify the Acids**: The acids we are considering are HI, HBr, HCl, and HF.

2. **Understand Acid Strength**: The strength of these acids increases as we move down the group in the periodic table. This is due to the bond dissociation energy; as the size of the halogen increases, the bond between hydrogen and the halogen becomes weaker and easier to break.

3. **Order of Acid Strength**:
- HI is the strongest acid among the four because it has the lowest bond dissociation energy.
- HBr is the second strongest.
- HCl is weaker than HBr.
- HF is the weakest acid because of the strong bond between H and F.

Therefore, the order of acid strength is:
\[ HI > HBr > HCl > HF \]

4. **Relate Acid Strength to Reactivity**: In the reaction \( R-OH + HX \rightarrow RX + H_2O \), a stronger acid will more readily donate a proton (H⁺) and thus will be more reactive. The nucleophilicity of the conjugate bases (I⁻, Br⁻, Cl⁻, F⁻) also plays a role, where weaker conjugate bases (from stronger acids) are better nucleophiles.

5. **Conjugate Base Nucleophilicity**:
- I⁻ (from HI) is the best nucleophile.
- Br⁻ (from HBr) is the next best.
- Cl⁻ (from HCl) is weaker.
- F⁻ (from HF) is the weakest nucleophile.

6. **Final Order of Reactivity**: Based on the acid strength and the nucleophilicity of their conjugate bases, the order of reactivity in the reaction \( R-OH + HX \) is:
\[ HI > HBr > HCl > HF \]

### Final Answer:
The order of hydrogen halide acids in decreasing order of reactivity is:
\[ HI > HBr > HCl > HF \]